Preferential accretion of binary stars

TL;DR

The paper tackles the problem of accurately modeling accretion onto unresolved binary stars in star-forming regions, where standard sink-particle treatments can produce unphysical fluctuations and suppression of accretion. It introduces a preferential binary accretion recipe that uses a virtual binary sink to determine how gas is accreted between the two components, guided by calibrated results from circumbinary disk studies and binary black hole simulations, and tracks a sink spin proxy during accretion. By applying this method in RAMSES with MHD and self-gravity, the authors demonstrate elimination of unphysical dips in accretion at periastron, smoother accretion histories, and improved convergence behavior across resolutions, while also highlighting limitations in low-$q_{\rm b}$ regimes and highly turbulent environments. The work enables more reliable global simulations of star-forming regions at coarser resolutions and provides a framework extendable to other unresolved accreting binaries, such as compact object binaries. Overall, the study advances the fidelity of binary accretion modeling in large-scale, multi-physics simulations with practical implications for multiplicity statistics and feedback in star formation.

Abstract

The attracting properties of gravity enable matter present in cores to collapse into stars with seven orders of magnitude change in space and time making modelling of star formation a challenging multi-scale process. To circumvent this scale problem stars are replaced by a sub-grid sink particle at a much larger scale. Sink particles are created above a threshold density and acquire mass and momentum through accretion. In models where binary star systems form and migrate to separations of a few cells, the accretion flow is unresolved and the relative accretion rate to the sink particles may become inaccurate. We introduce a new recipe for accretion onto binary sink particles that have overlapping accretion regions and implement an algorithm to track the angular momentum of sink particles as a proxy for the stellar spin. Our preferential binary accretion recipe uses a virtual binary sink particle for the purpose of accretion and redistribute the accreted mass onto the sink particles according to results from models investigating binary accretion in detail. This solves problems common to current algorithms in many codes: (i) accretion is not suppressed due to large velocity differences between gas and stars, when that velocity is only internal to the binary system, (ii) the accretion rates are smoother for the unresolved close binaries in eccentric orbits, and (iii) non-physical suppression of accretion onto the secondary sink particle when the primary dominates the potential is eliminated. We test our implementation by comparing simulations at increasing resolution until the binaries are resolved. While not perfect, it mitigates undesired properties of current algorithms and in particularly for global models of starforming regions. It may also be applied to other unresolved accreting binaries, such as compact objects in clusters and binary supermassive black holes in cosmological models.

Figures (15)

• Figure 1: Plot of $\lambda = \dot{m}_s / \dot{m}_p$, the ratio of accretion onto the secondary and primary star, against the mass ratio of in the binary $q_{\rm b}=m_{\rm s} / m_{\rm p}$. The data is merged from Siwek2023 to the right of $\rm q_{\rm b} = 0.1$ and Eq. \ref{['eq: preferential accretion']} which is adapted from Kelley2019. The left side of the plot continues to $\rm q_{\rm b} = 0$, but has been limited for a clearer view.
• Figure 2: The total and individual accretion rates for the pair 257, 260 at levelmax = 14. In blue is shown the original algorithm, while in red is the evolution with the new algorithm. The sink pair exhibit order of magnitude changes in the individual accretion rates over an orbit with the original algorithm. The distance between the sinks in AU is shown as the dashed line and on the right y-axis. The pair has an average eccentricity of 0.5 and a mass ratio of 0.9.
• Figure 3: The total (a), primary (b), and secondary (c) integrated masses of the sink pair 257, 260 over different resolutions from levelmax = 14 to 18. The origin is set to where the levelmax = 18 run started.
• Figure 4: The total (a), primary (b), and secondary (c) accretion rates of pair 257, 260 over different resolutions from levelmax = 14 to 18. The distance between the sinks in AU is shown on the right y-axis. The pair has an average eccentricity of 0.5 and a mass ratio of 0.9.
• Figure 5: The average $\lambda$ of each pair in each run against the mass ratio. The colour symbolises the resolution of the run it comes from and the symbol which pair it is. Lines are from Fig. \ref{['fig: preferential accretion']}.